MWD What’s So Special about Special Relativity

Special Relativity has to do with Einstein’s question, as a young man, of what the world would like to look like if you could run next to a beam of light. A question for which Physics had no answer. This article is about how Einstein discovered the answer to this question, and the implications of his answer. It is presented without delving deeply into the science and without utilizing mathematics.

As a Patent Clerk, 2nd class, at the Swiss patent office in Bern Switzerland (from 1902–1909), his job required him to punctually show up for work where a stack of patent applications was waiting on his desk for him to review. He was responsible for reviewing the patent applications for any scientific problems or inconsistencies, and if he found any problems or inconsistencies the patent application was rejected. Otherwise, it was passed on to the Patent Clerk (1st class) who reviewed the application to determine if another patent conflicted with it. He was so good at this job that it only took him a few hours to go through the stack of patent applications that was assigned to him for the day. He, therefore, worked on a few of the patent applications, then paused to read physics journals and think about what he had read. He would then review a few more patent applications, pause, and read and think ad infinitum throughout the day. This allowed Einstein plenty of time to keep current with what was happening in the world of physics. In 1904 he started concentrating on three subjects concerning physics; the existence of atoms, the photoelectric effect, and special relativity. In 1905 he had his “Annus Mirabilis” (Miracle Year), in which he published four papers on these three subjects (and the fifth paper in 1906), which resolved these subjects. The question of Special Relativity is the subject of this article.

I should point out that I am NOT a scientist or engineer, nor have I received any education or training in science or engineering. This paper is the result of my readings on this subject in the past decades. Many academics, scientists, and engineers would critique what I have written here as not accurate nor through. I freely acknowledge that these critiques are correct. It was not my intentions to be accurate or through, as I am not qualified to give an accurate nor through description. My intention was to be understandable to a layperson so that they can grasp the concepts. Academics, scientists and engineers’ entire education and training is based on accuracy and thoroughness, and as such, they strive for this accuracy and thoroughness. When writing for the general public this accuracy and thoroughness can often lead to less understandability. I believe it is essential for all laypersons to grasp the concepts of within this paper, so they make more informed decisions on those areas of human endeavors that deal with this subject. As such, I did not strive for accuracy and thoroughness, only understandability.

Isaac Newton’s Space as a Rubik’s Cube and Linear Time

Isaac Newton envisions space and time as four-dimensional. Each piece of space had a fixed length, width, and height (as three dimensions), and time (as the fourth dimension) which move linear (from past to present to future) at a constant rate such as a metronome (tick-tock, tick-tock, tick-tock, tick-tock).

This view of the universe would be replaced by Einstein’s Special and General Theory of Relativity, which interrelated space and time into spacetime, and made space flexible and time variable (relative spacetime).

Albert Einstein’s Relative Spacetime

Einstein was very punctual in arriving at the patent office, as was required at that time. He took the same trolley every day, at the same time, from his apartment to the patent office, and he even sat in the same seat each day. As this trolley pass by the Town Center on the way to the patent office Einstein was looking forward in his trolley ride to the center of town, and he often looked at the clock tower to think about the physics of time. After passing the Clock Tower he would start looking at the patent office and think about what he was going to read that day. One day, due to a family issue, he missed his regular trolley and had to catch the next trolley. This time he was facing away from the Clock Tower when he approached the town center, and when he passed the Clock Tower he was facing the clock. He began to wonder what's a clock would show if he was riding on a beam of light instead of a trolley.

He realized that as he traveled faster and faster it would take the next beam of light, that showed the next minute, longer to overtake the beam of light he was traveling on and therefore the clock would appear to run slower. He also realized that if he was traveling at the speed of light the next beam of light would never overtake him, and for all intents and purposes, time stood still for a beam of light. He then looked over his shoulders and realized he was traveling so fast that his apparent length to a stationary observer would be contracted. He then looked over his back and realized that the entire universe would slowly collapse in front of him as he was traveling toward the speed of light, eventually into a single point in the direction of travel when he reached the speed of light. He also realized that as he was traveling faster toward the speed of light that it would take more and more energy to speed him up, and that it would take all the energy in the universe to get him to the speed of light. This meant that mass could never be accelerated to the speed of light (all these effects will be explained further in this article).

This was an astounding insight and Einstein was very excited about it. He rushed to his desk in the patent office and immediately went through a stack of patent applications, and then stopped reviewing the patent applications and started doing the mathematics of his insight. By noon he had the answer mathematically and scientifically, and he stated it was one of the most exhilarating moments of his life, as that he knew something about the universe that no one else knew. Upon further work on this Insight, he realized that not only did Time, Length, and Mass change relative to your speed, but that different observers at different places traveling at different speeds could look at the same phenomena and report back different observations of what they had seen because of this effect. He named this phenomenon Relativity (which we now know as Special Relativity to distinguish it from General Relativity, which he developed a few years later). His science and math were based on Maxwell’s equations of electrodynamics, and Maxwell's equations were one of the few things that survived from classical physics because of this. He also realized that as a result of this phenomena mass and energy were equivalent, which resulted in his famous equation: E=mc2.

Einstein would continue to publish papers on the impacts of his insights, but he was generally ignored. After all, who could take seriously an unknown, unaffiliated, physicist from Bern Switzerland (he took pains to hide his occupation as a patent clerk)? Max Planck, however, took an interest in his Special Relativity and other prominent physicist started reviewing his work. In 1907 several light experiments were performed in which only Einstein’s Photoelectric Theory could explain the results. More physicist started taking him seriously, and by 1909 it was recognized that he was a genius (which allowed him to leave the patent office and become an associate professor of Theoretical Physicist at the University of Zürich). His previous papers were then studied and incorporated into the new field of Quantum Physics, and it is generally recognized that his “Annus Mirabilis” was the pivotal year in the break between Classical and Modern Physics.

Einstein’s "On the Electrodynamics of Moving Bodies" (Special Relativity) dealt with linear motion (motion in a straight line). As to the dynamics of the motion of bodies on a curved surface, Einstein developed his Theory of General Relativity. Soon after publishing the Special Theory of Relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework. In 1907, beginning with a simple thought experiment involving an observer in free fall, he embarked on what would be an eight-year search for a relativistic theory of gravity. After numerous detours and false starts, his work culminated in the presentation to the Prussian Academy of Science in November 1915 in what is now known as the Einstein field equations. These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present, and form the core of Einstein's General Theory of Relativity. This subject is explored in my paper “An Outline of Gravitational Physics”.

The Effects of Special Relativity

In physics, Albert Einstein's 1905 theory of special relativity is derived from first principles now called the Postulates of Special Relativity. Einstein's formulation is said to only require two postulates, though his derivation implies a few more assumptions.

The idea that special relativity depended only on two postulates, both of which seemed to be unavoidable, was one of the most compelling arguments for the correctness of the theory (Einstein 1912: "This theory is correct to the extent to which the two principles upon which it is based are correct. Since these seem to be correct to a great extent, ..."). The Postulates of special relativity are:

Time Dilation

Time dilation is a difference in the elapsed time measured by two observers, either due to a velocity difference relative to each other or by being differently situated relative to a gravitational field. As a result of the nature of spacetime, a clock that is moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference. A clock that is under the influence of a stronger gravitational field than observers will also be measured to tick slower than the observer's own clock. To you, the light beam, which was bouncing at the same spot before, now begins to move in a zigzag path. The faster the movement, the longer the length light travels and the length of time of one tick seems.

As can be seen in the diagram consider d as 186,282 miles (or d is one second). For the stationary observer, they will measure the time it takes for a beam of light to travel the distance d as one second. However, for an object that is moving the light beam must travel further to reach d, so that the time it takes for the light beam to reach d is greater than for the stationary observer. Someone inside the moving object d would still measure the time as one second for them, as d is still one second.

The effect of this is that when you are moving very very very very fast your time seems to be running at a normal rate for you, as you are measuring time in your frame of reference. However, a stationary observer would think that your time is running much slower, as they are measuring your time in their frame of reference. Therefore, if you had a twin who took a very fast and very long space journey and then returned your twin would be younger than you, as their time elapsed would be less than your time elapsed.

The Twin Paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as moving, and so, according to an incorrect and naïve application of time dilation and the principle of relativity, each should paradoxically find the other to have aged less. However, this scenario can be resolved within the standard framework of special relativity: the traveling twin's trajectory involves two different inertial frames, one for the outbound journey and one for the inbound journey, and so there is no symmetry between the spacetime paths of the twins. Therefore, the twin paradox is not a paradox in the sense of a logical contradiction.

Inside a Gravitational field, since the higher position is moving faster in relation to a lower position it leads to the following humorous situation.

This difference has actually been measured from the perspective of an accurate clock on an airplane as compared to the same accurate clock at sea level. This difference is very important for the Global Positioning System (GPS) as the GPS satellites are much higher than the ground receiving stations (such as your cell phone). If you do not account for the time difference between the satellites and the cell phone you will not get an accurate position (your actual position it can be up to 1.5 miles different).

The diagram above illustrates why a satellite travels further at the same time as an Earth traveler. However, the General Theory of Relativity states that mass distorts spacetime, and this distortion is primarily responsible for the clock differences in the above situation.

Length Contraction

Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. This contraction (more formally called Lorentz contraction or Lorentz–FitzGerald contraction after Hendrik Lorentz and George Francis FitzGerald) is usually only noticeable at a substantial fraction of the speed of light. Length contraction is only in the direction parallel to the direction in which the observed body is traveling. For standard objects, this effect is negligible at everyday speeds and can be ignored for all regular purposes, only becoming significant as the object approaches the speed of light relative to the observer.

However, it took Einstein to fully understand its full significance and embed it into the Special Theory of Relativity. The principle can be stated succinctly as follows:

The length of an object in a frame in which it is moving is shorter than the length of the same object in a frame in which it's at rest.

This phenomenon is physically real, and not an illusion, trick-of-the-light, nor due to actual errors in measurement or faulty observations. The object is actually contracted in length as seen from the stationary reference frame. The amount of contraction of the object is dependent upon the object's speed relative to the observer.

Therefore, when a stationary observer is measuring the length of an object moving at relativistic speeds they must account for this contraction. When both the observer and the observed are moving at relativistic speeds both of their lengths are contracted and must be accounted for.

Mass Increase of Objects

Mass in special relativity is of two different types; Inertial Mass and Relativistic Mass. Inertial Mass is primarily used in General Relativity to determine the curvature of spacetime, while Relativistic Mass is used in Special Relativity to determine the force need to move an object at high speeds (noticeable starting at approximately 20% of the speed of light but always present at any speed). In Special Relativity you must utilize Relativistic Mass. The major difference between the two is that Inertial Mass is basically rest mass, while Relativistic Mass is mass that is in motion. The reason you must treat them differently is that in applying a force to accelerate a mass the faster the mass is moving the more force needs to be applied to accelerate the mass. At slower speeds (relative to light speed) this difference is negligible and unmeasurable and was not noticed until Einstein’s Special Relativity pointed out the differences.

A somewhat inaccurate analogy would be the acceleration of a car. For this thought experiment, you need to differentiate the rate of change (acceleration) from the actual speed of the car (miles per hour). When you first start the car and begin to accelerate the car would respond and accelerate rapidly. As your speed increases, you need to apply more force to accelerate the car to a faster speed. When your car is speeding fast you need even more acceleration force to speed up the car. If you are paying close attention to the speed of acceleration you would notice that at a faster speed you are accelerating at a slower rate. In this car analogy, the real reason for this phenomenon is the power capabilities of the motor and the efficiency of transferring its power to the wheels of the car (mostly). In the physics of mass acceleration, it is entirely due to the amount of force needed to accelerate the Relativistic Mass. The faster the acceleration desired the more force must be applied.

Before Special Relativity when scientist and engineers measured the acceleration it appeared to occur linearly (a straight line). They assumed that this linearity would continue until you reached the speed of light (C). Einstein proved that this acceleration was actually a slope (logarithmic) in which the end would never reach the speed of light. Therefore, no mass could be accelerated to the speed of light as there would always be an insufficient force to achieve this goal. The following illustration graphs this phenomenon.

When Quantum Physicist utilizes particle accelerators to accelerate an atomic particle to perform experiments they must factor this phenomenon in their engineering to achieve their goals. Quantum particles are very small and of very low mass. Yet it takes a very large amount of energy (electromagnetic force powered by electricity) to accelerate a quantum particle near the speed of light. They can never accelerate a quantum particle to the speed of light. Besides the expense of building the equipment and instrumentation of a particle accelerator when quantum physicists perform an experiment, they run up a very large electrical bill. This is why particle accelerators are very expensive to build and operate. This is also why most modern particle accelerators require a multi-national effort to finance the construction and operation of the particle accelerator.

Different Observers – Different Observations

One of the consequences of Special Relativity is that different observers, in different motions, can observe different results for the same phenomenon, known as Relativity of simultaneity. This is due to the “Frame of Reference” for each observer must be accounted for. Some everyday example for a Frame of Reference is as follows.

If I tell someone that a car is moving on the highway from left to right it can mean a different thing to a different observer. For observers on my side of the highway, the car is indeed moving from left to right. For observers on the other side of the highway, the car is moving right to left. You must always account for the location of the observer (i.e. the Frame of Reference) for the observers to accurately describe the phenomena. Another everyday example is a ball bouncing on a moving train. To an observer on the moving train, the ball bounces straight up and down. To an observer on a station outside of the moving train, he would see the ball bounce up in a curve then down in a curve, due to the motion of the train. For an observer on a train moving in the opposite direction of the bouncing ball the arc would be compressed in the motion of travel of the. To accurately describe the motion of the ball you must define the Frame of Reference for the observer and the observed. The following diagrams illustrate these phenomena.

To illustrate this phenomenon of the Frame of Reference in Special Relativity, and its consequences, we will perform the following thought experiment.

In this thought experiment, we shall place an observer in the center, to the left, and to the right of a stationary train, and observers outside of the stationary train, as in the following diagram.

This stationary train will be struck by a lightning bolt with two forks, and each fork will strike the front and back of this train at the exact same moment of time to an inside and outside observer centered on the train. To the inside and outside centered train observer, this would be a simultaneous event. If the inside the train observer were not centered, but toward the back or front, the event would not be simultaneous. This is because the time it took the light from each strike to reach the back or front inside observer would depend on which direction they were offset. If they were closer to the front the light would have a shorter distance to reach them from the front and a longer distance to reach them from the back, and vice-versa. Only at the center would the lightning strike be simultaneous. As the shorter distance would take less time for the light to travel while the longer distance would take more time for the light to travel, the event would not be simultaneous to the back or front inside observers within the train.

To a stationary observer outside of the stationary train, it would not appear that the front and back lightning bolts struck at the exact same moment of time, depending on the position of the outside observer. If the outside observer were closer to the front or to the back of the train the light from the front or back lightning bolt strike has a longer or shorter distance to reach the outside observer. The longer distance would take a longer time and the shorter distance taking a shorter time to reach the outside observer. If the outside observer was centered on the train the light travel distance would be the same from both the front and back of the train being struck, and the outside centered observer would report a simultaneous event.

If the train were moving from left to right at very high speeds the outside center observer would report a simultaneous event, but the inside center observer would not witness a simultaneous event. As the inside center observer was moving very fast in the direction of the front of the train the light from the lightning strike from the front would reach them before the light from the back of the train, as they had moved closer to the impact point of the lightning (a lesser distance for the light to travel) and further from the impact point of the lightning from the back of the train (a more distance for the light to travel) when the lightning struck, as in the following diagram illustrates.

The times of the lightning strike of the back and front inside observers would also differ as they too were in motion.

There is also the phenomena of the center observer simultaneously flashing a light to a mirror at the front and back of the train and recording the return times, as in the following diagram.

In this phenomenon, a centered observer on the train would see the return time to be the same if the train were stationary or moving, as the total distance traveled for the light would remain the same (compare the stationary and moving train diagrams). On a moving train the inside observer would record the return time to be the same as the mirrors were also moving with the observer. It would take a longer time for the outgoing light to reach the front mirror (as it had moved forward), but a shorter time to for it to return as the moving observer had moved closer to the front mirror (and the opposite effect for the rear mirror). The total distance the light travelled would be the same for both the front and back flash, so the return time would remain the same for both the front and back flash. A stationary observer outside the train would see a different arrival time at the mirror depending if the train were stationary or moving. If the train were stationary the light from the back and front mirrors would arrive simultaneously for the stationary observer as they both traveled the same distance to the stationary observer. However, if the train was moving very fast from left to right the light from the front mirror of the train would arrive back to the stationary observer after the flash from the back mirror of the train, as it had a longer distance to travel

However, if the outside observer was moving in relation to the stationary event the times would always be different. To examine why this is so consider the following diagram.

When an observer is moving on a train, in any direction, and at any speed, and observes a stationary event the observer's motion changes their position relative to the stationary event. Therefore, the distances traveled by light from the stationary event changes with the motion of the observer. The faster the motion of the observer increases the distances for the light to travel from both of the events (front and back of the stationary event)) and therefore changes the times of each event (i.e. the greater the motion the greater the time differences). When you factor in that the observed event may not be stationary, but in motion, the distances and times for the event will change for everyone.

Of course, when you are dealing with objects as small and as slow as a train and the close distance of the stationary observer, and considering the high speed of light, these effects are not noticeable. You need very long objects (tens of thousands of miles long) travelling at relativistic speeds (see the following explanation), and a very far distance of the stationary observer (tens of thousands of miles away) for these effects to become noticeable. In the examples above instead of a train substitute a very long spacecraft travelling at relativistic speeds and a very distant stationary observer for a better example. However, modern precise scientific instruments can now measure these effects on smaller scale experiments that has shown Special Relativity effects on small scale phenomena.

This Frame of Reference effect in Special Relativity is known as “Loss of Simultaneity”. It is no wonder that the Loss of Simultaneity issue for physicist drove them bananas at the beginning of Special Relativity. But they have adapted and learned how to account for it in their observations, and it imposes no difficulty for today’s physicists.

Relativistic Speed

Relativistic speeds are required for the effects of Special Relativity to be discernable. At low speeds, they occur, but the effects are so minor as to be unmeasurable. At relativistic speeds, you must account for Special Relativity. So, what is a relativistic speed? The chart below illustrates the relativist effects (the curved line) at different velocities (the x-axis). The y-axis is the amount of relativistic effects. The upper left 1 is low-speeds (everyday effects), while the lower right 1 is the speed of light.

It takes relativistic speeds (because light travels very fast) or great distances between observers for the relativistic phenomenon to become apparent, which is why it was not discovered until Einstein proved that this would happen. It should also be noted that all observations of a relativistic event need to account for Time Dilation, Length Contractions, Inertial and Relativistic Mass, and Loss of Simultaneity as part of the observation.

E=mc2

When most people think of relativity they are usually thinking of Special Relativity. However, care should be taken to differentiate between General and Special Relativity. Although Special Relativity is incorporated into General Relativity, as a special case of General Relativity, physicists often differentiate the two based on the observations and experiments they are conducting.

When the general public thinks of relativity they often only think of the equation E=mc2. While E=mc2 is a consequence of Special Relativity it was not incorporated into the original paper describing Special Relativity. Several months after Einstein wrote his original paper on Special Relativity he wrote another paper which delineated some of the consequences of Special Relativity. One of these consequences was that energy was related to mass by the formula; energy is equal to mass times the speed of light squared (E=mc2). With this formula, even a small amount of mass could produce a very large amount of energy. Indeed, it is this formula that explains the massive amount of energy the Sun produces. The Sun converts mass (mostly hydrogen and helium) into other matter and releases energy as a result. There are many other factors in the Sun’s production of energy, but the limiting factor is E=mc2.

E=mc2 became famous as it is the equation utilized to create the Atomic Bomb and develop Atomic Reactors that produce electricity (now known as Nuclear Bombs and Nuclear Reactors – a much more accurate description). With the ushering in of the age of atomic power and atomic bombs, the general public became very familiar with the equation that was the basis for these events.

Miscellaneous Effects

There are other amazing or seemingly paradoxical consequences of Special Relativity that we need not go into in this article, not to mention it would take a book to explain them all. I’ll leave it to the reader to explore these consequences of Special Relativity if they so desire.

In my overview, I mentioned that when Einstein looked over his back and realized that the entire universe would slowly collapse in front of him as he was traveling toward the speed of light, eventually into a single point in the direction of travel when he reached the speed of light. This is not actually an effect of Special Relativity, but it is caused by the stars outside being blue shifted (due to the Doppler effect on light of high-speed motion) and shifted towards a point around your direction of travel (due to aberration). As these are astrophysics effects and not special relativity effects, they will not be discussed in this paper.

Final Thoughts

Einstein’s Special Relativity shook the very core of physics. It was no longer possible to make observations or conduct experiments, especially when dealing with atomic physics, electromagnetic radiation, and astrophysics without accounting for Special Relativity. Along with Einstein’s other contributions to physics, which were many and varied, Einstein and others ended the reign of Classical Physics and ushered in the age of Modern Physics. An age that we are still in and probably will be forever.

Albert Einstein Quotes:

Albert Einstein was one of the most quotable scientists, not only on science but life itself. I would like to end this paper with some of my favorite Einstein quotes as a tribute to this greatest scientist of the 20th century, as well as a great person of all time.

The Personal Website of Mark W. Dawson

Containing His Articles, Observations, Thoughts, Meanderings,
and some would say Wisdom (and some would say not).

What’s So Special about Special Relativity

The Meaning and Consequences of Special Relativity

Presented without delving deeply into the science and without utilizing mathematics.

Introduction

Isaac Newton’s Space as a Rubik’s Cube and Linear Time

Albert Einstein’s Relative Spacetime

The Effects of Special Relativity

Time Dilation

Length Contraction

Speed of Spaceship

Observed Length

Observed Height

Mass Increase of Objects

Different Observers – Different Observations

Relativistic Speed

E=mc2

Miscellaneous Effects

Final Thoughts

Albert Einstein Quotes:

Further Readings

Disclaimer

The Personal Website of Mark W. Dawson

Containing His Articles, Observations, Thoughts, Meanderings, and some would say Wisdom (and some would say not).

What’s So Special about Special Relativity

The Meaning and Consequences of Special Relativity

Presented without delving deeply into the science and without utilizing mathematics.

Introduction

Isaac Newton’s Space as a Rubik’s Cube and Linear Time

Albert Einstein’s Relative Spacetime

The Effects of Special Relativity

Time Dilation

Length Contraction

Speed of Spaceship

Observed Length

Observed Height

Mass Increase of Objects

Different Observers – Different Observations

Relativistic Speed

E=mc2

Miscellaneous Effects

Final Thoughts

Albert Einstein Quotes:

Further Readings

Disclaimer

Containing His Articles, Observations, Thoughts, Meanderings,
and some would say Wisdom (and some would say not).